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Signatures on semilocal rings

1972
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Bulletin of the American Mathematical Society
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We announce extensions of a part of the Artin-Schreier theory of real fields to semilocal rings. Detailed proofs will appear elsewhere. A always denotes a (not necessarily noetherian) semilocal commutative ring such that no residue class field has only two elements. A signature on A is a homomorphism a from the unit group, A*, of A to {± 1} with a{-1) = -1 and a(l 2 + am 2 ) = 1 for all triples (a, /, m) in A* x A x A such that I 2 + am 2 is a unit and cr(a) = 1. EXAMPLES, (i) If A is an

doi:10.1090/s0002-9904-1972-12852-0
fatcat:rq5irfe63fejth4wpthil5l6ea